Well now I'm curious: what's the limit of G<n> as <n> goes to infinity?
A truncated sine wave? (insofar as sine waves are their own derivative, shifted by 90 degrees, so if I'm doing my math right they would theoretically be G∞-continuous)
A truncated sine wave? (insofar as sine waves are their own derivative, shifted by 90 degrees, so if I'm doing my math right they would theoretically be G∞-continuous)